Research Paper on Heat Transfer

Introduction

Heat transfer refers to the mode of exchange between different fluids having varying temperatures occurring in engineering practices. Heat transfer is as simple as the exchange between hot and cold liquids moving in the same or opposite directions via a concentric tube.

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A lab experiment carried out to determine heat flow rates as well as temperature measurements via a heat exchanger. These measurements help work out rate of heat transfer and the heat transfer coefficient. The report aims to establish the heat transfer coefficient error based on the lab test.

The overall heat transfer coefficient is the most critical aspect in the analysis of heat transfer between two fluids. Overall heat transfer coefficient may be given by the equation using the Log Mean Temperature Difference method:

UA=qTLM and TLM = T1-T2ln(T1T2)

Hence: T1 = Th,i - Tc,i, T2 = Th,0 - Tc,0q is a total measure of heat exchange between cold and hot fluids, given by: q=mccp,c(Tc,o- Tc,i)

Counter flow:

TLM =(4.04815+3.99786+2.64717+2.8954)4 =3.397145 UA = 0.29436q

Parallel flow:

TLM = (2.85002+3.00904+1.87138+2.26537)4 = 2.4989525 UA =0.400167q

The thermal conductivity of stainless steel can give overall heat transfer coefficient:

In counterflow:

UA = 0.29436q, q =mccp,cTLM, mc =0.2 kg/s, cp,c =4267 J/kg.J, k =16.2 W/M2 .K, A =20.256m2

UA = 0.29436*0.2*4267*16.2 = 4069.55/20.256 therefore; U = 200.901 W/M2K

In parallel flow:

UA =0.400167*0.2*4267*16.2 =5532.34/20.256; U = 273.121 W/M2 K

Uncertainty in temperature measurement in experiment 1,2 and 3

For example, 31.1, 27.2, 29.9 degrees F

=87.98, 80.96, 85.82 F in such a case we use a 2 cause of the uncertainty of the exact value hence

87.982, 80.962, 85.822

The theoretical values 200.901 W/M2K and 273.121 W/M2 K are more exact as compared to the experimental value. The latter is as a result of errors such as experimental errors and errors that occur when analyzing the lab experiment. Error analysis is carried out to minimize errors as much as possible.

There is a slight disagreement between theoretical and measured values. Theoretical use mathematical concepts that are error-free hence an almost perfect amount is achieved. The theoretical values got by assuming ideal conditions while measured values obtained in a not so excellent condition.

Pre-lab solutions

Determination of heat transfer coefficient

Assumptions in this case we use oil as the fluid flowing hence properties include:

Cp = 2131J/Kg. K, mc = 0.25 GPM, k =0.138 W/m.K (Bergman and Frank 386)

h =mc cp =0.25*2131 = (532.75*0.138)/0.0209 = 3517.67 W/m2.K

With a flow rate of 0.5GPM

= (0.5*2131*0.138)/0.0209 = 7035.35 W/m2.K

Determination of heat transfer coefficient of flow through an annular pipe

DO =1.380''= 0.0351m, Di =1.050''=0.02667m, flow rate 0.25 and 0.5GPM, Pr = 4.85

ReD =4mp(Do-Di)m = 4*0.25p0.0351+0.02667*3.25*10-2 = 158.56

NuD = 0.023 ReD4/5Pr0.4 = 0.023*57.56*1.88 = 2.49

hi = NuDkDi =2.49*0.1380.02667 = 12.88 W/m2..K

ho =2.49*0.1380.0351 = 9.79 W/m2..K

Determining the overall heat transfer heat coefficient

DO = 1.38'' = 0.0351m, Di =0.824'' = 0.0209m

U = 11hi+ho = 1112.88+9.79 = 22.67 W/m2..K

Summary

Heat transfer is reviewed under the fundamental laws of heat exchange; these include conduction, radiation, and convection. Heat transfer through convection of fluids is given more emphasis in the report. The report based on results got theoretically and through lab tests conducted using different materials.

The objective of the report is to enable the reader to understand; the convective heat transfer, how to analyze counterflow and parallel flow tube-in-tube heat exchangers and the impact of uncertainty on data analysis. Flow rates and temperatures are measured and used to achieve a difference between experimentation and theoretical work. Heat transfer or exchange carried as an experiment shows a variation to theoretical values obtained through calculations. To eliminate errors analysis must be done to reduce errors. This helps to bridge the gap between actual or accurate data got theoretically through mathematical concepts.

Equipment used in the lab test include; concentric tubes or pipes through which water runs through. These pipes are made of stainless steel. The flow rate was periodically adjusted to test its effect on the fluid temperature; these temperatures are therefore noted down for calculation and comparison purposes. Two separate methods used to in the flow of the fluids, these are parallel flow and counter flow. Each set of test is repeated four times and temperature at each instance taken.

Conclusion

In conclusion, we are in a position to tell why there is a difference in theoretical transfer against its experimentation through the determination of overall heat transfer coefficient. This helps us to establish optimal conditions to ensure very accurate results with minimal errors. Error analysis can now be carried out with ease.

Works Cited

Bergman, Theodore L., and Frank P. Incropera. Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.